Predicting Grizzly Bear Density in Western North America
Garth Mowat1*, Douglas C. Heard2, Carl J. Schwarz3
1 Natural Resource Science Section, Ministry of Forests, Lands and Natural Resource Operations, Nelson, British Columbia, Canada, 2 Fish and Wildlife Section, Ministry of
Forests, Lands and Natural Resource Operations, Prince George, British Columbia, Canada, 3 Department of Statistics and Actuarial Sciences, Simon Fraser University,
Burnaby, British Columbia, Canada
Abstract
Conservation of grizzly bears (Ursus arctos) is often controversial and the disagreement often is focused on the estimates of
density used to calculate allowable kill. Many recent estimates of grizzly bear density are now available but field-based
estimates will never be available for more than a small portion of hunted populations. Current methods of predicting
density in areas of management interest are subjective and untested. Objective methods have been proposed, but these
statistical models are so dependent on results from individual study areas that the models do not generalize well. We built
regression models to relate grizzly bear density to ultimate measures of ecosystem productivity and mortality for interior
and coastal ecosystems in North America. We used 90 measures of grizzly bear density in interior ecosystems, of which 14
were currently known to be unoccupied by grizzly bears. In coastal areas, we used 17 measures of density including 2
unoccupied areas. Our best model for coastal areas included a negative relationship with tree cover and positive
relationships with the proportion of salmon in the diet and topographic ruggedness, which was correlated with
precipitation. Our best interior model included 3 variables that indexed terrestrial productivity, 1 describing vegetation
cover, 2 indices of human use of the landscape and, an index of topographic ruggedness. We used our models to predict
current population sizes across Canada and present these as alternatives to current population estimates. Our models
predict fewer grizzly bears in British Columbia but more bears in Canada than in the latest status review. These predictions
can be used to assess population status, set limits for total human-caused mortality, and for conservation planning, but
because our predictions are static, they cannot be used to assess population trend.
Citation: Mowat G, Heard DC, Schwarz CJ (2013) Predicting Grizzly Bear Density in Western North America. PLoS ONE 8(12): e82757. doi:10.1371/
journal.pone.0082757
Editor: Marco Festa-Bianchet, Université de Sherbrooke, Canada
Received January 7, 2013; Accepted November 5, 2013; Published December 18, 2013
Copyright: ß 2013 Mowat et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits
unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Funding: This work was funded by BC Ministry of Environment and the British Columbia Grizzly Bear Trust Fund. The funders had no role in study design, data
collection and analysis, decision to publish, or preparation of the manuscript.
Competing Interests: The authors have declared that no competing interests exist.
* E-mail: [email protected]
of grizzly bear abundance can be generated by assigning densities
based on expert opinion regarding the value of landcover
attributes, supported by, or in conjunction with, field estimates
derived in similar ecosystems [5]. No expert-based models to date
have estimated confidence limits for the resulting density estimates
so evaluating conservation risk was subjective. Expert models have
not considered fundamental concepts, such as whether microsite
attributes sum or scale up to provide an indication of landscape
scale density [6]. In spite of their shortcomings, expert-based
models have been used in all jurisdictions in Canada where grizzly
bear hunting is allowed [5,7–9].
2. Resource selection function models can be used to predict the
absolute or relative probability of occurrence [10,11] and possibly
density [12] within small ecological units. Although occurrence
models may be statistically explanatory and objective, considerable
subjectivity may be required when deciding how and where to
apply them (e.g., [10]). Models vary with the local availability of
resources and behaviors related to regional life history or human
influence, and they do not generalize well to other landscapes
[11,13–17]. This is a considerable problem given that grizzly bears
occupy a wide range of environments and have many different life
history strategies.
3. Trend data can be used to predict density from areas with
known abundance [18]. This method requires relatively precise
measures of trend that are independent of variation in bear
Introduction
Grizzly bear hunting is controversial because of peoples’
conflicting values and interests. Sarewitz [1] argued that progress
toward solving environmental controversies must come primarily
from political processes rather than from scientific research. He
regards the idea that scientific facts and theories will help settle
disputes or build the appropriate foundations for guiding
environmental policy as old-fashioned and suggests that the role
of science is to collect information to support the implementation
of policies determined through political processes. Where grizzly
bear hunting opportunity is managed by a quota system, a
maximum allowable kill rate is prescribed (the policy) which is
then applied to estimates of population size (the scientific
information). This paper describes an approach to predict grizzly
bear densities that can be used to support, monitor, and evaluate
policy decisions.
In the last 15 years, improvements in aerial survey [2] and
genetic identification techniques [3] have led to a proliferation of
grizzly bear density estimates [4]. However, due to the high cost
and the vast areas involved, field-based density estimates have
been and likely will continue to be restricted to a small subset of
hunted populations.
Three approaches for predicting grizzly bear density have been
proposed where field-based estimates are unavailable. 1. Measures
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Predicting Grizzly Bear Density
support the importance of any form of social regulation on density
[47].
Humans limit grizzly numbers by direct mortality, habitat loss,
and displacement due to disturbance. Mortality obviously reduces
density temporarily, but the relationship between mortality rate
and density is complex due to the effects of age ratios and density
dependence on vital rates. Habitat loss, and environmental change
that completely precludes occupancy by grizzly bears, obviously
reduces density. Disturbance has been shown to reduce grizzly
bear density at fine scales (e.g., along road corridors and near
developments [48,49]), but the link between disturbance and
landscape scale population density, although largely accepted by
practitioners [50], has never been demonstrated empirically.
Human density may index the above 3 factors, but the functional
link to bear density is unclear.
In this paper we modeled the relationship between existing
grizzly bear density estimates and potential limiting factors. We
then use those relationships to predict grizzly bear density across a
large and varied portion of their Canadian range and demonstrate
how the use of these predictions for setting hunting quotas and
evaluating past levels of human-caused mortality can support the
process of developing grizzly bear conservation policy.
abundance. These data were provided by moose hunters in a
Swedish example [18]. Similar data do not exist in North America
and we were hence confined to one of the two modeling
approaches.
For the greatest general application, predictive abundance
models must be underpinned by an understanding of the
functional processes affecting density, use direct measures of
resource abundance, and apply to all environments and life history
strategies [19]. Recent work has quantified relationships between
abundance and landscape scale measures of environmental
attributes for white-tailed deer (Odocoileus virginianus; [20]),
carnivores [21], tassel-eared squirrels (Sciurus aberti) [22], coyotes
(Canis latrans) [23], kangaroos (Macropus spp.) [24] and people
[25]. Most of these models included one or more measures of food,
indexed either by a direct measure of the resource, such as tree
basal area for squirrels, or remote measures, such as temperature,
precipitation and soil type for humans.
We considered both bottom–up (food supply) and top-down
(competition and predation) influences on grizzly bear abundance.
Grizzly bears are omnivores and their reliance on animal protein
varies greatly across their range [26–28]. The single largest meat
source in their diet in coastal areas is spawning salmon and all
areas of very high bear density have large numbers of salmon over
much of the non-denning season [2,28]. Many populations have
no access to salmon and in the continental interior, grizzly bears
eat plants, especially fruit, and supplement their diet with insects,
rodents, freshwater fish, and ungulates where available [26–28].
Bears prefer highly digestible plant species and parts, because they
have a simple stomach and are relatively inefficient at digesting
plant matter [29,30]. Preferred species of plants where bears eat
the vegetative structure can be considered hydrophilic and bears in
the interior concentrate their foraging in moist sites [27,31]. The
exception being when they are digging for corms or roots of
various plants. Fruits of several shrubs are highly preferred in late
summer and fall and, along with meat, are the basis for the fat
deposition required for winter hibernation [32]. The abundance of
grizzly bear foods is not only related to ecosystem productivity but
also, for bears that live in forested environments, to successional
stage [33].
Competition may limit grizzly bear density where they are
sympatric with black bears (Ursus americanus) [34,35]. Black
bears and grizzly bears have similar digestive and foraging
efficiencies [30,36,37] and any competitive advantage of black
bears over grizzly bears feeding on plants and fruits is based largely
on the smaller body size of black bears [30,37]. Where grizzly
bears rely on meat, they often appear to exclude black bears from
the meat source [2,38,39], probably because the meat source is
clumped and therefore defendable, unlike plant and fruit supplies.
Areas that are largely devoid of trees do not support black bears
where their range overlaps that of grizzly bears [2,26,34,39,40].
Presumably grizzly bears exclude black bears from large open
areas because black bears cannot seek refuge from grizzly bear
aggression by climbing trees [34,40,41]. Historic persecution levels
may also influence potential competition between the two bear
species and this may be mediated by reproduction in grizzly bears
[42]. Reproduction is higher in black bears than grizzly bears
[34,35].
Grizzly bears have no significant predators [43,44], but social
factors may limit bear numbers. For example, female bears may
avoid important feeding areas to minimize the chance of male
bears killing their offspring [45,46]. Several different hypotheses
have been proposed regarding social regulation in grizzly bears
[44], however a recent analysis of field data for 4 sites did not
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Materials and Methods
Model development
Based on previous research we felt that the following factors
may functionally influence grizzly bear density at the population
scale: plant productivity, vegetation type, fish and meat availability, scramble competition with black bears, human disturbance,
and human-caused mortality. Based on this functional model, we
began by assembling and deriving indices for these factors while
attempting to choose measures that were not highly correlated
with other factors to avoid collinearity (Table 1). Variables that
described food limitation were: salmon availability, the proportion
of salmon or ungulates and other non-plant foods in the diet,
remote sensing measures of plant productivity, and the proportion
of the landscape covered by trees and herbaceous vegetation.
Competition with black bears may be best described by measures
of black bear abundance, but these were so few that we used tree
cover or simple presence or absence of black bears as surrogates
for more direct measures of competition.
The only mortality factor we considered was direct killing by
people. Although it has been mandatory to report all humancaused deaths in all jurisdictions in North America since the
1970’s, a substantial proportion of that mortality goes unreported
[51] including traditional use by First Nations. The direct effect of
human-caused habitat loss in urban areas was accounted for in the
remote sensing vegetation measures above. We used human and
livestock census information as measures of both the loss of habitat
effectiveness, due to behavioral decisions of bears to avoid areas
frequented by humans and, the impact of unrecorded humancaused mortality. Other surrogates, such as road density or the
number or proportion of problem grizzly bears killed, were
difficult to standardize across jurisdictions and were more
temporally variable. We did not consider predation, diseases,
parasites, or social limitation, because there is no evidence that
those were general limiting factors. Hence our three over-arching
hypotheses were based on food limitation, scramble competition
with black bears, and human limits to density via mortality, habitat
loss, and decreased habitat effectiveness.
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Predicting Grizzly Bear Density
Table 1. Factors hypothesized to limit grizzly bear density in interior ecosystems in North America and the
variables we derived to index these factors.
Plant productivity
Vegetation type1
Diet
Competition with
black bears
Human disturbance
Human-caused mortality
annual precipitation
tree10
salmon presence
tree10
tree10
human density
annual temperature
tree25
%salmon in diet
tree25
tree25
human+livestock density
annualized NDVI
herb50
%terrestrial meat in
diet
black bear presence
livestock density
human+livestock density within
10 km2
evapotranspiration
herb75
human density
human+livestock density within
50 km2
ruggedness
herb100
human+livestock density
mean recorded human-caused
mortality in past 10 years
human+livestock density within
10 km2
human+livestock density within
50 km2
We digitized the study area boundary for each study area and calculated the average for each index using a GIS. See Table S1 in Appendix S1 for detailed description of
GIS derived variables.
1
This is the sum of all pixels with .the stated percentage of described cover. For example, herb50 = the proportion of the study with pixels rated as .50% herb/shrub.
2
This is the mean human and livestock (sheep and cattle) density (summed) for the area within 10 or 50 km of the study area boundary.
doi:10.1371/journal.pone.0082757.t001
contemporary forces that work to exclude grizzly bears from parts
of their range. We selected areas of similar size to other studies in
those ecosystems and derived measures for independent variables
as for occupied study areas. Though the density estimate was zero,
based on local knowledge, we assigned upper CLs based on
trapping results, non-hunter kills and the recent record of bear
sightings in the study area.
We revised all grizzly bear density estimates by removing the
area of water, rock, and bare ground, because we considered these
unsuitable to bears.
The dependent variable - meta analysis of grizzly bear
abundance
We critically reviewed estimates of grizzly bear population size
or density in the published and unpublished literature. We were
interested in estimates for landscapes large enough to represent a
grizzly bear population affected largely by births and deaths rather
than immigration and emigration, so we only used data where
study area size was .800 km2 (range 789–22,875 km2) or
approximately 10 female home ranges, and contained at least 15
resident bears (^
x = 80, range 15–765). We used all population
estimates that met the above criteria and where we judged the
authors had done enough field sampling to generate an estimate
that was indicative of the ecosystem. We noted whether authors
accounted for bears that were not detected during fieldwork,
which generally required the use of mark-recapture analysis, but
we accepted more subjective assessments for some intensive census
studies. We also noted whether authors had accounted for closure
bias, which is the positive bias caused by movement in and out of
the study area during the study. We indexed the accuracy of each
population estimate by standardizing the confidence limit (CL)
width as a percent of the point estimate so we could weight each
observation in the analysis. We arbitrarily doubled the width of the
reported upper confidence limit (UCL) if authors did not consider
incomplete detection (3 areas) or the lower confidence limit (LCL)
if authors did not account for closure bias (2 areas). Where no
measure of precision was given, we assigned CLs based on survey
effort. We arbitrarily assigned the LCL as 50% of the point
estimate, but if the authors considered closure bias we reduced the
LCL to 25% of the estimate. We doubled the point estimate to
index the UCL unless the authors accounted for incomplete
detection explicitly, in which case we reduced the UCL to 50% of
the point estimate. We created confidence limits using the above
ad-hoc rules in 52 of 109 observations including all 16 unoccupied
areas discussed below and these were larger than most probability
based limits.
We selected 16 study areas in places that were historically
occupied by grizzly bears, but were currently not occupied. These
areas were all adjacent to occupied areas and there was no known
barrier to dispersal. We chose these areas to represent the range of
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Independent variables - derivation of surrogates for
limiting factors
We derived average annual precipitation, average annual
temperature, NDVI, and evapotranspiration to index plant
productivity from freely available spatial databases (Table S1 in
Appendix S1). Study area boundaries were digitized and mean
values for each variable were calculated for each study area,
excluding open water and barren areas, which was up to 35% of
the study area (mean = 6.5%). For five study areas outside of our
precipitation map, we used data from the nearest Environment
Canada long-term weather records.We also derived a measure of
topographic ruggedness [52], which we included as a covariate to
index the increased land area associated with sloped areas. This
variable was correlated to precipitation (r = 0.73, N = 90), but not
to any other productivity variables (r,0.28, N = 90).
Landcover had been previously assigned into 3 structural classes
at 500 m resolution: herbaceous (which includes shrubs ,2 m in
height), trees .2 m tall, and barren ([53]; Table S1 in Appendix
S1). We surmised that in areas where the two bear species are
sympatric, grizzly bears would monopolize resources in open areas
and we used the proportion of each study area which was tree
covered to index inter-specific interaction, while recognizing that
the lack of tree canopy may also increase the vegetation resources
available to bears. We calculated the proportion of forest in the
vegetated portion of each study area by summing the proportion of
pixels rated as .25% forest. We derived a measure of herb-shrub
cover to index vegetative forage under the general assumption that
forage is more abundant in non-forested areas. We calculated the
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proportion of herb-shrub area by summing the pixels with .50%
herb-shrub cover. Pixels that were rated as 100% barren were
excluded from spatial calculations (using a GIS mask); these areas
were mostly rock and ice.
We used the fraction of salmon and animal tissue in the diet of
bear populations as surrogates for salmon and terrestrial meat
availability. Diet fractions may not be linearly related to resource
availability, but deriving measures of salmon and meat availability
across large areas was not feasible. Salmon and terrestrial meat
components of the diet were predicted using isotope analysis of
grizzly bear hair collected from each study area [54]. Where we
did not have hair samples to estimate diet, we calculated mean
values from spatial raster-based maps built from a continent-wide
diet dataset ([54], digital data available in SOM). Unoccupied
areas were necessarily assigned diet fractions in this way. We based
diet fractions on direct feeding observations for two study areas
(Nome and Midsu), because the model predictions suggested no
salmon in the diet, and this was known to be incorrect [2]. For one
area (Tweedsmuir), we recalculated diet using just the samples
collected in the study area, because the map-derived values
included areas where salmon were not available and were likely
inaccurate. We also applied this value to the nearby KimsquitDean area, because the mapped diet was likely biased low due to a
drastic decline in salmon numbers in the nearby Owikeno Sound
([55] and unpublished data). Kokanee (Oncorhynchus nerka) were
considered part of the salmon component of the diet. Kokanee diet
fractions presented in Mowat and Heard [54] were reduced by
half, based on further data collected from kokanee in central
British Columbia (D. Heard, unpublished data). We also derived a
categorical variable indexing the importance of salmon where 0
meant no salmon available, 1 for areas with little salmon, such as
some interior areas, and 2 for those areas where bears were
considered to derive most of their resources from salmon.
Human and livestock density was used to index human
displacement, disturbance, and unreported bear mortality. We
tested log transformations of these variables, because the influence
was expected to be nonlinear [56]. The number of people and
livestock (cattle and sheep) were calculated from polygon-based
census data for the US (2000) and Canada (2001). Count data
were used to calculate density for each census unit and density was
used to calculate the number of resident people and livestock in
each study area. In order to minimize the number of variables we
added the human, cattle and sheep counts together to produce a
single composite variable; this index combined both the various
human impacts with the threat of direct mortality posed by
livestock grazing.
Human-caused mortality necessarily reduced bear density and
was entered directly and as a squared term to account for the nonlinear influence of recent mortality on the standing population. We
estimated the number of bears killed by people from government
databases or published accounts. Counts of all legally killed bears
have been recorded since at least the mid 1970s for all the
jurisdictions in this study and represent a minimum number of
bears killed by people. We calculated the annual kill rate (number
bears killed/bear population estimate) over the 10 years previous
to each density estimate. Unoccupied areas were assigned mean
kill rates so these records did not bias the fitting of this variable.
Raw data are available in Appendix S2.
because of the difficulty in interpreting the resulting regression
equation [58].
Ordinary least squares regression cannot be used directly to fit
these models, because of the inclusion of study areas where no
grizzly bears were located. For these points, the assumption of
normally distributed errors about the regression line is violated.
Consequently, Tobit regression [59] was used. In this model, a
latent (hidden) variable (Y *) follows the ordinary linear model:
Y ~X bze
However, only the max(0, Y *) can be observed, i.e. it is
impossible to observe negative densities.
Maximum likelihood was used to fit the Tobit model (Proc
QLIM, SAS 9.2). Models were fit where every study area was
given equal weight and where study areas were weighted by the
inverse of the relative CLs to downweight study areas with less
precise estimates of density.
We constructed an a-priori suite of models based on expert
judgment, including variables thought to affect grizzly bear
densities. Additional models were added to the initial model set
where potential predictors were dropped or transformed.
Potential models included transformed values for human and
livestock density to approximate the known form of the
relationship, based on previous research as described earlier. We
also included indicator variables that controlled for 3 cases we
considered outliers, based on initial screening of the data. Two
study areas had high and presumably unsustainable mortality
rates, and one unoccupied area had very high human density. We
used the small-sample corrected AICc to compare model fit,
ranked models using AIC weights [60], and we examined topranked models for the presence of uninformative variables [61].
We investigated the leverage of each record in the top-fitting
models using influence plots based on simple regression to check
for individual study areas that may account for the inclusion of a
predictor in the model. Residuals from the top-fitting models were
examined for outliers and distribution [57].
We used a leave-one-out jackknife procedure to estimate the
increase in prediction error that might occur when the model was
used to predict densities outside of the set used to build the model.
Each individual study area was sequentially dropped from the
analysis, the remaining data were used to fit the model being
examined, and this fitted model with sample size n-1 was then used
to predict density for the study area held out.
Results
We derived 118 estimates of density including 16 for areas
currently unoccupied by grizzly bears (Tables 2 and 3). This total
included 2 repeated inventories for 6 study areas that were carried
out in different years. The number and precision of those
inventories was greatest in the southeastern portion of the range
of grizzly bears and lowest in Yukon and the Northwest Territories
(Figure 1). We do not believe there was a systematic bias in the
data based on the selection of study areas because the motivation
for inventories was not just conservation concern. Inventories were
done for research, impact assessment, native land claims,
ecological benchmarks and trend monitoring in National Parks.
In coastal areas, where salmon were abundant (i.e., .27% of
diet), grizzly bear density estimates were up to an order of
magnitude higher than in interior areas (Figure 2). In addition,
coastal grizzly bear density estimates were much higher in areas
where black bears were absent than where they were present
Statistical analysis
We used Principal Components Analysis (PCA; [57]) to contrast
.3 variables that were surrogates for the same limiting factor.
Principal component scores were considered, but not used,
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Table 2. Descriptive statistics for data used to build models to predict grizzly bear density in interior North
America.
Variable
Occupied areas
Unoccupied areas
x
SD
Min
Max
n
x
SD
Min
Max
n
Population size
92
96
15
765
76
0
0
0
0
14
Study area size
(km2)
5110
4297
789
22875
76
6358
1629
3913
8959
14
Barren (% of study
area)
6.7
8.6
0.0
34.6
76
1.7
2.1
0.1
6.7
14
Density (barren area
removed)
23.0
15.1
2.5
64.6
76
0.0
0.0
0.0
0.0
14
CL relative (% of
density)
1.0
0.5
0.1
1.9
76
0.8
0.3
0.5
1.0
14
Human-caused
mortality (%)
3.7
3.9
0.0
20.1
76
01
0.0
0
0
14
Annual precipitation
(cm)
84
40
16
199
76
52
7
43
68
14
NDVI
116
15
77
137
76
129
5
115
136
14
AET
296
104
97
443
76
342
60
228
440
14
Average annual
temperature
24.0
5.0
217
3.7
76
0.9
3.1
25.0
4.7
14
Ruggedness
3.9
1.4
1.0
6.0
76
2.2
1.3
1.0
4.2
14
Trees (.25% per
pixel)
48.1
34.7
0.0
99.5
76
69.7
30.0
8.4
99.7
14
Herb-shrub (.50%
per pixel)
57.6
28.1
3.1
99.1
76
50.6
28.4
6.8
94.0
14
Salmon (% of diet)
1.0
3.0
0.0
14.0
76
1.5
3.6
0.0
10.2
14
Kokanee (% of diet)
0.7
3.5
0.0
26.0
76
0.6
1.5
0.0
5.1
14
Meat (% of diet)
25.1
15.5
0.0
58.2
76
29.3
13.9
12.5
48.1
14
Human density
(humans/km2)
0.9
1.7
0.0
8.4
76
4.3
5.6
0.0
21.4
14
Livestock density
(animals/km2)
1.7
5.5
0.0
39.4
76
11.5
16.9
0.0
53.2
14
See Table S1 in Appendix S1 for detailed description of GIS derived variables.
1
The kill rate in unoccupied areas was zero, but we used the mean rate of 3.7 for occupied areas during analysis so that these areas did not bias the distribution for this
variable.
doi:10.1371/journal.pone.0082757.t002
In interior areas, the first eigenvector of a PCA suggested all 5
vegetation productivity variables were correlated and that
ruggedness and NDVI contrasted in the second eigenvector.
These results suggested ruggedness and NDVI should be included
in the multivariate analysis, but that any of the five productivity
variables could substitute for one another. For this reason we
decided to include all five variables in the analysis. A second PCA
with the vegetation type variables also demonstrated strong
correlation among 4 of the 5 variables, whereas the fifth variable,
herb100, was nearly invariant across the data. These results
suggested that any one of the vegetation type variables could be
used to index vegetation cover. We chose herb50, because we felt
it would index bear food with the most sensitivity. We also
included tree25 in the global model to index black bear
competition, which was supported by comparing black bear
presence across vegetation cover. Although the vegetation cover
variables were strongly correlated, the presence of black bears was
most clearly separated across the tree25 variable (Figure 3). A third
PCA for the human influence variables showed essentially a single
component that was an average of all 5 variables. Both human and
livestock density showed a threshold with density, which suggested
(Table 3). The one exception was the Kuskowim Delta in
westcentral Alaska. This area had modest grizzly bear density
and their diet contained more terrestrially derived meat (presumably caribou) than salmon or vegetation (C. Stricker, USGS,
Denver, unpublished data). Coastal areas where black bears were
present had much lower grizzly bear density, and the proportion of
salmon in the grizzly bear diet was also more variable (Table 3).
We concluded the availability of salmon led to fundamentally
different ecological relationships so we built separate models for
coastal and interior areas based on an arbitrary cut-off of 20%
salmon in the diet. We further separated the coastal data into those
areas where black bears were sympatric with grizzly bears and
those where black bears were absent. We did not build a predictive
model for coastal areas where black bears were absent because
there were no areas like this in British Columbia.
In interior areas, density varied from 2.5 to 65 grizzly bears/
1000 km2 and there was a broad range of values for most
independent variables (Table 3). Human and livestock density was
higher for unoccupied areas, presumably because humans were
the ultimate cause of the extirpation in many of these areas.
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Predicting Grizzly Bear Density
Table 3. Descriptive statistics for data used to predict grizzly bear density in coastal North America.
Variable
Black bears present
Black bears absent
x
SD
Min
Max
n
x
SD
Min
Max
n
Population size
81
88.6
0
352
17
619
450
102
1548
11
Study area size
(km2)
3743
2858
431
9854
17
2829
2463
228
9163
11
Barren (% of study
area)
16.0
10.4
0.7
43.4
17
9.6
10.0
1.1
35.7
11
Density (barren area
removed)
31.1
25.9
0
86.6
17
332
215
37
856
11
CL relative (% of
density)
1.1
0.5
0.1
2.0
17
0.6
0.5
0.2
1.5
11
Human-caused
mortality (%)
2.3
2.6
0.0
10
17
3.8
2.7
0
7.3
11
Annual precipitation
(cm)
275
111
115
473
17
160
57
101
255
11
11
NDVI
109
16
75
130
17
104
12
79
115
AET
370
58
263
474
17
321
30
239
351
11
Average annual
temperature
1.6
2.5
22.6
6.7
17
1.0
2.0
24.5
2.6
11
Ruggedness
5.5
0.6
4.2
6.2
17
4.3
1.0
2.6
5.4
11
Trees (.25% per
pixel)
54.4
23.1
17.8
96.8
17
40
25
1
79
11
Herb-shrub (.50%
per pixel)
44.9
16.6
8.8
71.6
17
68
21
36
98
11
Salmon (% of diet)
41
22
0
78
17
59
15
28
82
11
Kokanee (% of diet)
0.4
0.8
0.0
3
17
0
0
0
0
11
Meat (% of diet)
2.3
3.9
0.0
13.4
17
3
11
0
36
11
Human density
(humans/km2)
4.3
13.4
0.0
55.0
17
0.6
1.6
0.0
5.5
11
Livestock density
(animals/km2)
1.1
4.3
0.0
17.9
17
0.01
0.00
0.0
0.02
11
We separated areas where black bears were absent, because there were large difference in density between these areas. See Table S1 in Appendix S1 for detailed
description of GIS derived variables.
doi:10.1371/journal.pone.0082757.t003
a non-linear relationship. We excluded the 2 variables that
measured human and livestock density surrounding each study
area, because there was no indication that density trended to zero
at high human or livestock density [56].
There was very little variation in salmon in diet (which included
kokanee) in interior areas and so the composite of fish and
terrestrial meat in the diet was dominated by the meat component.
For this reason the food composite variable was not considered
further in the analysis.
In coastal areas with black bears, a PCA for the vegetation
productivity variables yielded similar results to the interior dataset
and we considered all five variables for the same reasons as above.
We also chose to include herb50 and tree25, because these two
variables may contrast herbaceous food abundance with competition with black bears. Human density was the only human
influence variable that had substantial variation across the dataset
and was the only variable we included. Diet was dominated by
salmon and this was the only diet variable considered (Table 2).
Expectedly, there were no coastal areas with low precipitation
(Table 2).
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Tobit regression for interior areas
Based on biological considerations and the above investigation
of the data, we included the following variables in our global
regression: precipitation, NDVI, AET temperature, ruggedness,
herb50, tree25, salmon-in-diet or salmon-presence, meat-in-diet,
human density, livestock density or human + livestock density,
human-caused mortality, and (human-caused mortality)2. Log
transformations were also compared for the human-influence
variables. When we compared the effect of salmon-in-diet versus
the salmon-presence variable, only the salmon-presence variable
remained consistently in the top models and we therefore excluded
the salmon-in-diet variable.
When we compared the prediction strength of ‘human and
livestock density’ versus the single composite variable, the
composite variable was not included in the top-competing models.
A log transformation did not improve the fit of the composite
variable. This suggests the form of the relationship between
human density and bear density differed from that of livestock
density and bear density, so we dropped the summed variable,
‘human plus livestock density’.
One unoccupied area had double the human density of the next
lowest value and was considered an outlier. This study area
(Thompson) and the two other study areas (Upper Susitna and
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Predicting Grizzly Bear Density
Figure 1. Estimates of grizzly bear density in North America. Areas currently unoccupied are filled with hatching. The presence of black bears
throughout the study area is denoted by a black outline, partial presence of black bears by a gray outline and a hatched gray or no outline means
black bears did not occur on the study area. Areas without salmon are not colour filled, those with abundant salmon are filled in red, and those where
salmon were present but not abundant in rose. The black bear distribution in North America is shown in tan [91].
doi:10.1371/journal.pone.0082757.g001
inclusion of tree cover (2), the proportion of terrestrial meat (2) in
the diet, and the exclusion of NDVI. Rankings of models were
relatively consistent between the weighted and unweighted
analysis and we present only the weighted analysis here.
Residual plots, using Model 2, showed no evidence that the
regression assumptions were not met [57]. There was considerable
variation in the residuals, but the largest residuals were associated
with the observed densities with the widest CLs (Figure 4). For
computational ease, ordinary least squares was used to compute
approximate partial regression plots (leverage plots, [62]). These
showed no serious outliers. The standard error of all predictions
was approximately 10.5 bears/1000 km2. Two thirds of the CLs
of the observed densities overlapped the 1:1 line (Figure 4). Model
errors were assumed to be independent among study areas. For 4
of the 90 study areas, the observed estimate fell outside the
approximate 95% prediction interval for that site, but in all cases,
the CL for the observed estimate overlapped the CL for the
regression (Figure 4).
Swan Hills), where the number of grizzly bears killed by people
was very high, were modeled using indicator variables in order to
test their influence on fit. No models that included these indicator
variables were included in the top models, suggesting these cases
did not unduly leverage the analysis (Table 4). ‘Salmon-presence’
and ‘meat-in-diet’ were usually in the top models and the
regression coefficient for the salmon variable was positive,
whereas, surprisingly, that of the meat variable was negative.
The weighted Tobit models gave highest AIC weight (18%) to
the global model, but this model had 9 variables, whereas the next
model, that had only 7 variables, had similar weight (17%) and an
AIC value that was only 0.3 higher than the global model. We
chose to exclude the global model on the basis that it contained
noise parameters and considered Model 2 to be our best model
(Table 4). Model 2 included: annual precipitation (sign positive),
annualized NDVI (+), average annual AET (+), the proportion of
pixels in the study area with more than 50% herb-shrub coverage
(+), log human density (2), livestock density (2), and ruggedness
(+). The top 3 models had similar weight and differed by the
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Predicting Grizzly Bear Density
Figure 2. The relationship between grizzly bear density and mean annual precipitation. Study areas where grizzly bears were allopatric
are denoted by squares and where black and brown bears were sympatric by diamonds. Open symbols denote coastal study areas where salmon was
a major component of the diet; filled symbols show study areas where salmon were few. Unoccupied areas and one coastal area where brown bears
were allopatric and at very high density (856) are not shown.
doi:10.1371/journal.pone.0082757.g002
The mean model error for all jackknife runs was compared to
the mean error of the model with all data included. For the top 10
interior models, the mean squared prediction error was 9–13%
greater using the jackknife procedure compared to the model fit
using all of the data. Model 1, the global model, which we
excluded, had 12% higher model error using the jackknife
procedure compared to the model error based on all the data
whereas Model 2, our preferred model, had 9% higher error
Figure 3. The relationship between vegetation cover and grizzly bear density. These are 76 sites from across interior North America where
salmon is a minor component of the diet. We compare this relationship between 2 variables, tree cover (a–b) and herb-shrub cover (c–d). We also
present 2 levels of summary within each study area for each variable. For example, tree.10% means that we summed the pixels where tree cover
was .10% and calculated the proportion of the study area where this occurred. Black bears appear to be absent from areas where grizzlies are
present and trees cover , about 20% of the study area. The proportion of the study with .25% tree cover appears to best describe this process.
doi:10.1371/journal.pone.0082757.g003
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Predicting Grizzly Bear Density
Table 4. The top 10 model selection results for study areas in interior North America (n = 90) relating grizzly
density to variables that were hypothesized to be functionally related to density.
Model number
Model description
AICc
DAICc
K
AICc weight
2
Prcp_NDVI_AET_H50_LHum_Live_Rug
978.9
0.0
9
0.17
3
Prcp_NDVI_AET_H50_T25_LHum_Live_Rug
979.0
0.1
10
0.16
4
Prcp_AET_H50_Meat_LHum_Live_Rug
979.1
0.3
9
0.15
5
Prcp_NDVI_AET_H50_T25_Meat_LHum_Live
980.1
1.2
10
0.09
6
Prcp_NDVI_AET_H50_T25_SP_Meat_LHum_Live_Rug
980.2
1.4
12
0.08
7
Prcp_NDVI_AET_H50_SP_Meat_LHum_Live_Rug
980.5
1.6
11
0.07
8
Prcp_AET_H50_SP_Meat_LHum_Live_Rug
981.2
2.3
10
0.05
9
Prcp_AET_H50_T25_Meat_LHum_Live_Rug
981.5
2.6
10
0.05
10
Prcp_NDVI_AET_H50_T25_SP_Meat_LHum_Live
982.6
3.7
11
0.03
11
Prcp_AET_H50_T25_SP_Meat_LHum_Live_Harv_Rug
982.8
3.9
12
0.02
The top-ranked model was excluded from this list, because it contained 2 uninformative variables. Variables are: Prcp = precipitation, NDVI = normalized differential
vegetation index, AET = actual evapotranspiration, H50 = herbaceous and shrub cover .50%, T25 = tree cover .25%, Meat = terrestrial meat in diet, SP = presence of
salmon in diet, LHum = log human density, Live = livestock density, Harv = human-caused mortality, Rug = ruggedness.
doi:10.1371/journal.pone.0082757.t004
(Table S2 in Appendix S1). The increase in prediction error for
the interior dataset was modest and indicated that predictions for
study areas outside those used in fitting the model should be
reliable. Model-averaged predictions and predictions from Model
2 were similar and further justified considering it our best model
(Figure S1).
Tobit regression for coastal areas
Based on biological considerations and the above investigation
of the data, we included the following 7 variables in our global
regression: precipitation, NDVI, AET, temperature, ruggedness,
herb50, tree25, salmon-in-diet, and human density or log human
density. The top model in the weighted Tobit analysis had 7
variables and the second model had 6 variables (Table 5). We
excluded both models, based on the sample size to parameter ratio
and because the third model included only 3 variables and the
AIC value was only 2.2 higher than the top model, suggesting the
other 4 variables in the top model were largely uninformative [61].
Our preferred model included the proportion of pixels in the study
area with more than 25% tree cover (2), the proportion of salmon
in the diet (+), and ruggedness (+). Rankings of models were
relatively consistent between the weighted and unweighted
analysis and we present only the weighted analysis here.
The jackknife procedure was also used to compare among
coastal models. The mean square prediction error from the
jackknife models varied from 30–112% greater than that of the
fitted model; it was 30% higher for Model 3, our preferred model
(Table S3 in Appendix S1). Because the coastal model was based
on a relatively small number of data points, compared to the
number of predictors, Models 1 and 2 may have been fitting
artifacts of the coastal study areas.
Residual and leverage plots using Model 3 showed no evidence
of lack of fit and no serious outliers. Plots of predicted versus
observed densities showed a modest variation of residuals
(Figure 5). Model averaged predictions and Model 3 predictions
were similar, further justifying our use of Model 3 to predict
density (Figure S2).
Figure 4. Observed versus predicted values of grizzly bear
density (bears/1000 km2) using the best fit interior model
described in Table 4. Data included 76 inventoried study areas and
14 unoccupied areas across the interior of western North America. Error
bars are 95% confidence limits for observed data derived from the
survey results or estimated subjectively, based on survey methods (see
Methods for detailed description). The cases with the largest residuals
often had the greatest error and were hence weighted lower in the
regression.
doi:10.1371/journal.pone.0082757.g004
can be derived from density and these can be added to derive a
population prediction for a larger area. We could not compute
estimates of the uncertainty in composite predictions (i.e. for the
total over several prediction areas), because predictions for study
areas that are geographically adjacent with similar covariate sets
are unlikely to be independent. Combining the uncertainties of the
individual predictions will underestimate the uncertainty of the
total. Without further information about the spatial structure of
predictions from neighboring geographical areas, it is unclear how
to compute an appropriate measure of uncertainty for the total
over multiple study areas.
We predicted grizzly bear densities for Canada by summing the
individual predictions within wildlife management units (Table 6).
We used the interior Model 2 for all areas except coastal British
Model predictions
Our models can be used to predict grizzly bear density for any
area for which data exist for the input variables. Population size
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Table 5. The top 10 model selection results for study areas where grizzly and black bears were sympatric in coastal
North America (n = 17) relating grizzly density to variables that were hypothesized to be functionally related to
density.
Model number
Model description
AICc
DAICc
K
AICc weight
3
T25_salmon_Rug
157.7
0.0
5
0.17
4
Prcp_NDVI_AET_salmon_Hum_Rug
157.8
0.1
8
0.16
5
Prcp_NDVI_AET_salmon_LHum_Rug
158.0
0.3
8
0.15
6
Prcp_NDVI_Temp_H50_salmon_Hum_Rug
158.8
1.2
9
0.10
7
Prcp_NDVI_Temp_H50_salmon_LHum_Rug
159.9
2.2
9
0.06
8
Prcp_NDVI_Temp_H50_T25_salmon_Rug
160.2
2.6
9
0.05
9
Prcp_NDVI_Temp_T25_salmon_Hum
160.7
3.1
8
0.04
10
Prcp_NDVI_H50_T25_salmon_LHum_Rug
160.9
3.3
9
0.03
11
Prcp_NDVI_H50_T25_salmon_Hum_Rug
161.2
3.5
9
0.03
12
NDVI_T25_salmon_Rug
161.2
3.5
6
0.03
The two top-ranked models were excluded from this list, because they contained four and three uninformative variables. See Table 4 for definition of variables; salmon
= salmon in diet.
doi:10.1371/journal.pone.0082757.t005
a habitat sink for grizzly bears. The Dezadeash and Arkell units
have mortality rates .5% and may be of conservation concern.
Predicted densities for British Columbia varied from 0 to
58 bears/1000 km2. The highest coastal densities were in northern areas where salmon consumption was high and tree cover was
low. Interior areas with high density occurred throughout the
province, but were always rugged areas with high rainfall and few
people. Many units in the province were predicted to have low
density and, whereas this was often associated with high human
density, predicted densities in flat areas with low rainfall and low
herb-shrub cover were also low. The average rate of humancaused mortality was 2.9%/yr, with most mortality from hunter
kills (mean = 295/yr), but problem bear kills, and road and rail
collisions, (mean = 61/yr) comprised a greater proportion of
deaths in units with low predicted bear populations or relatively
high human density (Table S4 in Appendix S1).
Columbia where were used coastal Model 3 (Table S4 in
Appendix S1)
Predicted grizzly bear densities in the Northwest Territories and
Nunavut varied from zero in southcentral NWT to .30 bears/
1000 km2 in parts of the western arctic coast, densities decline to
the east and were much lower east of the Mackenzie River. In
Yukon, the model predicted densities that vary from 0–31 bears/
1000 km2 (Table S5 in Appendix S1). The lowest density was for
the Labarge Unit surrounding the city of Whitehorse; the only
place in the territory that had high human density. The Kluane
area of southwest Yukon had higher precipitation than the range
of data in the model (234 cm). This prediction may be biased high,
if the relationship with density is not linear, but rather levels off
beyond the range of the input data (Table 2). The average humancaused kill rate among population units was 1.3%, but was ,1%
when calculated for the entire territory. The Labarge unit had
about 3 kills/year and predicted density of zero. This area may be
Discussion
Model Tests
We lacked the data to systematically test our models independently, so our testing was confined to comparisons with other
approaches and examining areas of known low density. Boyce and
Waller [10] used RSF models from previous research in Montana
to predict potential abundance in the Bitterroot Mountains of
central Idaho. This area is currently not occupied by grizzly bears
so the number was meant to assess recovery potential. They had
models for 3 seasons. The lowest predicted abundance was 321
bears and their highest seasonal prediction was 484 bears in
spring. Our interior model predicted a total population of 657
bears (approximate 95% CL = 211–1103). Boyce and Waller [10]
assumed that the population estimate from their two reference
study areas were unbiased estimates of equilibrium density
whereas bear numbers have increased in both areas since their
research was done [63,64].
Mattson and Merrill [65] provided an independent prediction
of grizzly numbers in the Cabinat-Yak Recovery Area in Montana
and Idaho, based on study area scale modeling of habitat
capability and the depressive effects of human use. This area
was one of our model areas and the 2004 population was
estimated at 44 bears. The population was recovering from very
Figure 5. Observed versus predicted values of grizzly bear
density (bears/1000 km2) using the best fit coastal model
described in Table 5. Data included 15 inventoried study areas and 2
unoccupied areas across the interior of western North America. Error
bars are 95% confidence limits for observed data derived from the
survey results or, estimated subjectively based on survey methods (see
Methods for detailed description).
doi:10.1371/journal.pone.0082757.g005
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Predicting Grizzly Bear Density
Table 6. A summary of predicted numbers of grizzly bears in Canada and in National Parks by province, based on
the coastal and interior models developed in this paper.
Province
Predicted population size from this
Current population projection paper
Prediction units
Number in National Parks
Alberta
867a
1250
ecoregions
396
British
16,014b
13,131
WMU’s
126
Columbia
13,974
GBPU’s
14,101
ecoregions
Nunavut
1000c
8080
ecoregions
Northwest Territories
5100c
16,771
ecoregions
835
Yukon
6300c
10,404
guide territories
465
10,465
ecoregions
0
We predicted density for small portions of each province using ecological unit mapping (ecoregions-the largest units used), provincial wildlife management units
(WMUs), provincial grizzly bear population units (GBPUs, groups of 1–5 WMUs), and territorial guide territory boundaries which were roughly similar to WMUs in size.
[94] with corrections for portions of the National Parks that were not included.
b
[92].
c
[9].
doi:10.1371/journal.pone.0082757.t006
a
to have .150 bears (South Chilcotin Ranges, Squamish-Lillooet,
Toba-Butte and the North Cascades). A recent inventory in the
southern portion of the South Chilcotin Ranges unit suggests
current populations may be similar to predicted numbers and
hence no longer threatened [68]. The Squamish and Toba
populations are recovering from human over-exploitation and are
likely lower than predicted by the model. The North Cascades
area in southwest BC and central Washington currently supports
very few bears [69] although our model suggests the area may be
capable of supporting several hundred bears on the Canadian side
alone (Table 7). Previous habitat-based modeling suggested that
the Canadian portion of the North Cascades could support 293
bears [70], which is similar to the 284 suggested by our model.
Our interior model predicted grizzly densities between 19 and
35 bears/1000 km2 in the six recovery areas in the lower 48
United States. This resulted in population predictions between 64
and 874 per study area, which is many more bears than currently
occurs in two of these 6 areas (Table 7). As in Canada, the biggest
discrepancy was in the North Cascades. Additionally, the
Bitterroot Range is currently unoccupied, yet the interior model
predicted 445 bears in this unit. In both these areas recovery is
likely limited by the inability of grizzly bears to re-colonize these
areas, not habitat characteristics.
We compared prediction units of various size and the results did
not alter total population predictions for British Columbia or
Yukon greatly (Table 6). The impacts were greater for British
Columbia, because density was more variable. There are limits to
the size of the area to which the model can be applied; ideally
prediction units would be similar in size to the study areas used to
build the model.
low numbers and human-caused mortality appears to be limiting
recovery [66]. Mattson and Merrill’s model predicted the area
could support 123 bears and our interior model predicted 130
bears. The current population size may be a result of top-down
mortality forces and the predicted population sizes may be best
viewed as potential population sizes if the population was released
from top-down limitation.
Predictions for extirpated zones and depressed
populations as model tests
There were 14 study areas not known to support grizzly
populations in the interior dataset. The predicted density was zero
for 8 of these areas and .4 for the 6 other areas. Two areas had
predicted density of .14 bears/km2. Grizzly bears do not occur in
the southern boreal regions of NWT and Nunavut and northern
Alberta and Saskatchewan [9]. This area is presumably grizzly
bear-free naturally, because human density is very low. Four
unoccupied study areas in this area had low human density and
predicted grizzly bear densities were 0, 0, 9, & 21 (SE 10.6–10.8).
Predicted grizzly density for ecoregions in the unoccupied area
varied from 0 to 38 bears/1000 km2. The boreal portion of this
unoccupied area was predicted to have low bear density, usually
zero. The parkland and grassland areas south of the boreal zone
were predicted to have zero bears throughout Alberta, but high
densities were predicted in the same ecoregions in Saskatchewan.
Human and livestock densities were much higher in Alberta, all
other input data were similar. These results demonstrate that our
interior model does not index the ecological factor or factors
limiting distribution in all unoccupied areas well. Some combination of limiting factors excludes grizzlies from the Canadian
prairies and surrounding boreal forest and this result was only
correctly predicted by the interior model when human density or
tree cover was high.
We also used our preferred models to predict equilibrium
densities in known extirpated areas and zones with depressed
populations that are designated as threatened or endangered in
British Columbia and the lower 48 states ([8,67] Table 7). Areas
where grizzly bears are currently extirpated in British Columbia
were all predicted to have densities ,8/1000 km2 and ,30 grizzly
bears in the population unit. Most threatened units were also
predicted to have small populations, but four units were predicted
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Using the models to manage grizzly bear mortality
The models we developed, and the population sizes predicted
from them, provide information to support the implementation of
grizzly bear management policies. Population predictions were
used to calculate human-caused mortality limits and predict
habitat capability. Sustained yield management involves the tradeoff between conservation risk and benefits to society. Conservation
risk can be minimized by policy, such as reducing the maximum
harvest rate, or by investment, such as by increasing inventory
effort. In 1978 the Government of British Columbia began to
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Predicting Grizzly Bear Density
Table 7. Extrapolated grizzly bear densities and population sizes for a selection of areas in western North America
that are currently unoccupied, occupied at low densities, or are considered threatened.
Population unit
Current population estimate
Predicted population size
Okanagan Valley, BC
0a
27
Thompson Valley, BC
0a
13
Caribou Plateau, BC
0a
0
a
Peace River agriculture zone, BC
,40
North Cascades, BC
23a
284
Garibaldi-Pitt, BC
18a or 0b
40
Squamish-Lilloet, BC
56a or 52b
180
Toba-Bute, BC
75a or .106b
211
Stein-Nahatlach, BC
61a or 23b
129
South Chilicotin Ranges, BC
104a or .147b
257
Blackwater West Chilicotin, BC
193a
24
29
Granby-Kettle, BC
81
a
88
South Selkirks, BC
58c
85
Yahk, BC
20c
12
Bitteroot, ID and MT
0d
445
Cabinet-Yak, ID and MT
44d
130
North Cascades, WA
,5d
874
Northern Continental Divide, MT
765e
641
South Selkirks, ID and WA
30–40c
64
Yellowstone, WY, MT, ID
600f
567
Current population estimates were taken from government sources in British Columbia and the US and predicted population sizes were derived using our top coastal or
interior model.
a
[92].
b
[68].
c
[93].
d
C. Servheen, USFWS, Montana, pers. com.
e
[64].
f
[67].
doi:10.1371/journal.pone.0082757.t007
have to assign a density to the area either subjectively or using
some other method, and 3) the credibility of the modeling process
will be reduced, because it will be clearly evident that the model is
‘wrong’. These nuances and decisions are regularly confronted by
wildlife managers and our example highlights the fact that
removing subjectivity from the decision making process is
impossible, even for very well studied species. Our study
demonstrates the benefit of local knowledge, even for this highly
data-driven management system. For example, 15% of our data
were from extirpated areas where the population estimates and
precision were based on local knowledge.
The population predictions were higher than current estimates
for all Canadian provinces and territories except British Columbia
[9]. Much of the discrepancy can be attributed to the fact the
model predicted relatively high densities in northern boreal areas
as discussed earlier. Densities predicted by the interior model in
the tundra portions of the north are almost certainly too high in
the eastern Arctic where large areas are not currently occupied or
newly colonized. Population predictions for the Northwest
Territories and Nunavut may be more realistic if these unoccupied
areas were excluded from the prediction area.
Both our models predict more variable densities than other
modeling efforts in British Columbia [5,72] or Alberta [73]. If this
variation is real, then earlier models were over-predicting density
in some areas. Indeed, 12 management units in British Columbia
move from seasonal hunting restrictions to a quota system to
manage grizzly bear hunter kill. This change was effected in order
to reduce conservation risk and indeed there is evidence some
grizzly bear populations increased following to this policy change
([71] and G. Mowat, unpublished data), although other limiting
factors may have changed as well. The paradox of these good
intentions is that a quota system requires population sizes for every
hunted population, because allowable kill is usually calculated as a
portion of the standing population. Implementation of that policy
required population estimates for all areas occupied by grizzly
bears. This policy change precipitated a large increase in inventory
investment [4], but population predictions were still required for
many parts of the Province. The prediction method we describe
here was another response to the change in harvest policy, and a
reasonable balance between accuracy and investment. Our work
used all currently available data, did not require expensive field
testing, and provided predictions for all areas of British Columbia.
Our study demonstrates the uncertainty in extrapolating animal
densities, even for species for which there is considerable inventory
data and a good understanding of the population biology. Many
areas were predicted to be unoccupied, or nearly so, when clearly
this was not the case based on local knowledge or kill data, and
vice-versa. This presents 3 problems for wildlife managers; 1) they
will be forced to decide between those conflicting data (i.e.,
whether to allow hunting), 2) if they allow hunting then they will
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Predicting Grizzly Bear Density
was always positively related to density, even though there was
only a small range of variation in this variable. But, diet fractions
did not necessarily correlate directly with salmon abundance or
availability, especially where bears eat mostly salmon. In coastal
areas where black bears were absent, salmon consumption was
uniformly high (with one exception) and grizzly bear density was
almost an order of magnitude higher than coastal areas where
black bears were present (Table 3). Many observers have suggested
that body size increases with dietary meat (reviewed in [54]) and
although Mowat and Heard [54] showed that body size was
strongly related to the amount of salmon in the diet, it was less
correlated with terrestrial meat (see [28] for similar results).
Regardless of the strength of the relationship between diet and
body size, body size may be a better index of food quality or
abundance than population density. In Alaska, bears in hunted
areas were larger than bears in nearby ecologically similar areas
that were not hunted ([47], see also [81]). We conclude that
salmon availability influences grizzly bear abundance, but this
relationship may be more complex than a simple linear
relationship across the range of the species. Our data suggest a
negative relationship between density and terrestrial meat
availability, which may explain the observation by Mowat and
Heard [54] above, but this observation may also be due to
colinearity with other variables in our model.
Mattson and Merrill [56] and many others reported that human
density negatively influences grizzly bear density and that grizzly
bears cannot exist at a human density .7/km2. Our data
generally support this hypothesis; only 1 of 101 occupied areas had
human density .7/km2 and this study area straddled a heavily
settled valley, but did not sample a great deal of the less settled
mountains on either side of the valley. Mattson and Merrill [56]
showed that the probability of grizzly bear persistence was
inversely related to cattle density; similar to our findings that
density was inversely related to livestock numbers.
Reported human-caused mortality explained relatively little of
the variation in density when other factors were accounted for.
Our data did not suggest a non-linear relationship between density
and kill rate, as would be expected based on current theories of
population growth [82,83]. This was not too surprising given that
most kill rates in our dataset were low. Low kill rates may cause
little reduction in population size, especially when mostly males
are killed. It has been suggested that grizzly bear populations show
high compensatory responses only near ecological carrying
capacity [84]. Hunter kill may also have been compensated for
by immigration. Lags in the local impact of mortality due to
immigration would confound comparisons of instantaneous
measures of density and kill rate. Immigration sustained harvest
has been observed in Eurasian brown bears where male-biased
harvests may have indicated high immigration rates [85].
Similarly, populations that were reduced due to human-caused
mortality, but have not recovered for various demographic
reasons, would also confound the instantaneous comparison of
density and kill rate, as discussed earlier. Human or livestock
density may have accounted for some of the influence mortality
had on density, but this was likely small, because correlations were
weak between these variables in both datasets (r,0.07). Human
and livestock density may be correlated with unreported humancaused mortality, however.
appear to have annual kill rates higher than that allowed by policy
(6%). A further 15 units that had predicted densities of zero had
.2 reported bear kills annually during the past 8 years. This level
of kill suggests a resident population. However, many of these units
were predicted to have small populations. The above results could
be due to model imprecision and mortality would need to be
managed at larger scales to reduce this problem, as is currently
done in BC. Management responses to this new information must
occur on a unit by unit basis and incorporate other information
such as local knowledge about distribution and movement among
units; major food sources, such as salmon runs; hunter success; age
and sex ratio of past kill; trend in kill numbers; and the trend and
distribution of problem occurrences. We asked all regional
population managers to evaluate the model predictions against
all available data independent to the modeling process (Table 8). If
the evaluation criteria suggested the model prediction was
unrealistically low or high then we encouraged the manager to
interpolate a density from a similar ecosystem. At the provincial
scale, the mean predicted kill rate among wildlife units in British
Columbia was 2.9% for those units that were predicted to support
grizzly bears, which should be sustainable in most populations
[50].
Biological implications of the models
We demonstrate that grizzly bear density is related to general
indices of resources in the environment. Our results suggest that
ultimate factors, such as vegetation biomass and productivity,
vegetation structure, and protein abundance and availability,
influence grizzly bear density across its North American range. We
further show the degree to which density can be reduced by
human influences, other than hunting, although the limiting effect
of competition on density was equivocal. Other research has
demonstrated the link between forage abundance and population
growth in black bear [74,75] and grizzly bear populations
[28,63,76]. The negative effect of humans on grizzly bear
population growth was empirically demonstrated in the latter
two papers. Although the competitive effect of black bears on
grizzly bear population density has been suggested [35] including
potential individual and population level effects [77,78] and, a
potential mechanism described [42], demonstrating this effect on
population density or growth remains elusive.
Our results suggest the plant portion of the bear diet is indexed
by precipitation and NDVI. Precipitation likely indexes plant
productivity whereas NDVI is thought to index plant biomass
[79]. Ruggedness also appears related to density and, although it
was correlated with precipitation (r = 0.73), the PCA analysis
suggested these two variables contrasted in the third eigenvector,
suggesting some level of independence. Ruggedness may index the
increased surface area associated with sloped areas, which should
provide greater plant biomass and increased variation in plant
phenology among microclimatic sites [49]. A wide variety of
studies have found grizzly bears select for more rugged terrain
[11,16,33,49]. Density was negatively related to forest cover and
positively related to herb-shrub cover, presumably because bear
plant foods are more abundant in non-forested areas. Habitat
selection studies have demonstrated avoidance of forested areas by
grizzly bears [33,80]. However an alternative, and not exclusive
hypothesis using our data, is that fewer trees may benefit grizzly
bears by reducing competition with black bears. We could not
isolate these two effects in our analysis.
In coastal areas density increased as the amount of salmon in
the diet increased [28]. Our interior data also provide weak
support for the generality of this observation, because the salmon
presence variable appeared in 6 of the 10 top interior models and
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Alternative methods for predicting grizzly bear density
Our approach to predicting density differs from most previous
attempts that have usually been based on bear distribution or
movement data and applied a use-versus-availability analysis
approach [86]. This approach has been applied several times using
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Predicting Grizzly Bear Density
Table 8. Criteria used to evaluate individual model predictions that were independent of the model process.
Evaluation data required
Evaluation reasoning
Evaluation outcome
Anecdotal data including the locations
where bears were sighted
If the distribution or number of bears people
see is increasing this suggests an increasing
population
Sightings of sows with cubs suggest the unit is occupied; distributional
changes suggest corresponding changes in bear numbers; increased
sightings suggest an increasing population
Locations where bears were killed or
conflicted with people
The distribution of conflict or kill locations
over time may suggest expanding, static or
contracting bear distribution
Conflicts with sows and cubs suggest the unit is occupied; distributional
changes suggest corresponding changes in bear numbers; increased
conflicts suggest the population is increasing
Absolute ages of dead bears (from all
human caused mortality)
Females older than 7 years are likely residents
because they are unlikely to emigrate from
their home range
Presence of resident bears suggests the unit is occupied; older median
age at mortality of males suggests a lower kill rate
Age by sex of bears in the hunter kill
Trend in median age suggests a population
trend
Decreasing age of males or increasing age of females may signal a
declining population
Hunter success rates
Trend in success suggests a population trend
Higher success rates may indicate an increasing population
Proportion of females in the hunter kill
Trend in female proportion suggest a
population trend
Increasing proportion of females suggests a declining male population
These criteria can be used to confirm residency, to identify suspect predictions, evaluate a predicted level of harvest, or help decide what level of harvest to allow.
doi:10.1371/journal.pone.0082757.t008
Finer scale diet measures should improve the models and their
application.
The variables driving our model were largely static. A dynamic
model would require annual databases for each variable, such that
every variable would be an appropriate multiannual mean predating each survey. This would require vastly more digital data
and the elimination of much early bear density data, because most
databases begin in the 1980’s or later. An effort of this level should
also attempt to document human use of the landscape via a
dynamic measure of road abundance and distribution; this too
would require annual road layers for the past and the future. For
its current application, it is crucial that local practitioners of the
model understand its limitations so they understand where model
predictions are least certain.
We were unable to index the availability of terrestrial meat and
the correlation between precipitation and terrestrial meat in the
diet (r = 20.63) undermined our ability to evaluate this factor
using diet proportions. Also, the correlation of these two variables
with tree cover (rprecip = 0.33, rmeat = 20.35) negated a controlled
evaluation of the importance of competition with black bears
(ignoring the question as to whether the tree cover variable was a
reasonable index of competition). The availability of salmon was
not correlated to other independent variables, but salmon was not
a major contributor to diet in the interior. In the coastal model the
salmon diet proportions were quite variable and appeared sensitive
to changes in salmon availability [54,55].
We were unable, at the scale we worked at, to index key
vegetative foods like berries. Huckleberries (Vaccinium membranaceum) are a key food in most wetter environs and this resource is
linked to natural burns [88]. We could not find data to index
huckleberry abundance directly, nor could we find digital data that
documented burn history at the scale of the continent.
Density estimates may vary with the size of the area over which
they were measured [89,90] but we believe we avoided this issue
by selecting estimates based over large areas (Tables 3–4).
There were weak negative relationships between density and
area (r,20.59) in all 3 datasets, but we believe this is explained
by the need to have larger study areas in lower density
populations in order to meet sample size requirements. The
data we used were not subject to publication bias, a potential
radiotelemetry data from individual grizzly bears [10] or detection
data [11,65,73,80]. Although these studies used rigorous analysis
techniques, often accounting for multiple scales and contrasting
the importance of many different variables, the model structures
appear unique to the landscape of origin and the authors were
careful not to extrapolate the models much beyond the original
study area which were roughly the size of one grizzly bear
management unit in BC. Many models of this scale would be
needed to predict density for BC. All final models included
abstract landcover measures, such as elevation or greenness, that
likely had complex relationships with other variables and with
density, makings these types of models difficult to interpret in a
functional sense.
In contrast we followed a more functional approach using
measures of grizzly bear density at the landscape scale as
the dependent variable rather the presence or abundance of
individuals at a site. Density combines all the factors that
influence population dynamics in a single measure and should
be independent of factors such as individual behaviour which
influence the outcome of finer scale analyses. Our analysis
was unaffected by the relative abundance or availability of
different resources within a study area that can limit
predictions of an RSF model [17]. We consider the scale of
our approach more appropriate than behavior-based models,
because our dependent variable was measured at a similar scale to
which we hope to make predictions [87] and, our model
incorporated data across the entire area we intended to make
predictions.
Model weaknesses and improvements
Perhaps the largest weakness of our coastal model are the
salmon diet data. This was a key variable, but it was extracted
from a diet surface constructed from 81 diet measures across
northwest North America, and many fewer along the coast. We
augmented extracted data with local diet data where they were
available, but this was sporadic. Perhaps the most important
influence of the diet data on outcome was in deciding whether
prediction areas were coastal or interior. The main information we
used for this was the salmon diet data and when these were not
available we used local knowledge though this was incomplete.
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Predicting Grizzly Bear Density
meta-analysis problem, because we used both published and
unpublished data.
areas and 2 unoccupied areas across the interior of western North
America.
(TIF)
Supporting Information
Acknowledgments
Appendix S1 Supporting tables.
(DOC)
We thank the many scientists who shared their data and advice, especially
A. Hamilton, S. Miller, R. Sellers, E. Becker, R. Flynn, L. Van Daele, G.
MacHutchon, C. Apps, A. Laliberte, C. Servheen and C. Carroll. T.
Gaines and D. Pritchard skillfully did the GIS analysis. Thanks to B.
McLellan, C. Johnson, and J. Swenson for reviewing drafts of the
manuscript and B. Cadsand for help with formatting references. We
dedicate this paper to Tom Gaines who worked tirelessly on earlier
versions.
Appendix S2 Raw data.
(XLS)
Figure S1 Model averaging for the interior data. Model-
averaged predicted grizzly bear densities compared to predictions
from the top model in Table 4. Data included 76 inventoried study
areas and 14 unoccupied areas across the interior of western North
America.
(TIF)
Author Contributions
Conceived and designed the experiments: GM DCH. Performed the
experiments: GM. Analyzed the data: CJS GM. Contributed reagents/
materials/analysis tools: GM DCH CJS. Wrote the paper: GM DCH CJS.
Figure S2 Model averaging for the coastal data. Model-
averaged predicted grizzly bear densities compared to predictions
from the top model in Table 5. Data included 15 inventoried study
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